Has the Liar Said Anything?

Indexical regress — what is the referent statement?

>This statement is false
>This statement, “This statement is false,” is false
>…
>…
>This statement, “This statement, “This statement, “This statement, “This statement…”…” …is false,” is false,” is false,” is false,” is false
>…
>…

Propositional regress — what has been claimed?

>This statement is false
>That this statement is false is false
>That that this statement is false is false is false
>…
>…
>[…] that that that that this statement is false is false is false is false is false […]
>…
>…

Or better yet —

>[This statement is false]
>[[This statement is false] is false]
>[[[This statement is false] is false] is false]
>[[[[This statement is false] is false] is false] is false]
>[[[[[This statement is false] is false] is false] is false] is false]
>…
>…
>[[[[[[[[… [This statement is false] is false] is false] is false] is false] is false] is false] is false] is false] is false]…
>…
>…

What is the semantical provision that allows us to escape such a scenario —

Liar: “This statement is false”
Respondent: “What statement?”
Liar: “This statement is false”
Respondent: “What statement?”
Liar: “This statement is false”
Respondent: … (… ad infinitum)

— and why does it not yield the same problems that other self-referential statements such as “This statement has five words” seem to?